"Henry is hugely respected by the community that he works with and all that have known him and that's been indicative of the huge support he's had from both sides of the family," his cousin said.
Simon Worsp said Henry had spent time with Mr Dodds' father, David, and partner, Gabrielle Molloy.
There was no animosity between the families and Henry would be welcome at today's private service for "Dodzy" in Rotorua.
The support reflected a recognition that feelings of resentment would not help people to move on with their lives, Simon Worsp said.
However, the death weighed heavily on 35-year-old Henry, a husband and father of two young children.
Said his cousin: "When you're a loving, caring person and you, through an error of judgment, cause the death of somebody, it's a pretty hard thing to live with, I would imagine."
Simon Worsp described Henry as a "very honest young man with high integrity" who had grown up in an outdoor-loving family and in the past had a "healthy sense of humour".
Mr Worsp said that as a hunter, he had put himself in Henry's shoes.
"All hunters, when we see a tragedy, we revisit our own practices and we just have to keep to those very simple principles of positively identifying targets.
"But it does bring it all home to you that as a hunter you have a huge responsibility."
Meanwhile, Henry Worsp remains in limbo as the police decide whether to lay charges.
A police spokeswoman said the investigation into the shooting was expected to take several weeks to complete.
Mr Dodds is the third person to die in a hunting accident this year.
